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PDE methods for DWMRI Analysis and Image Registration

PDE methods for DWMRI Analysis and Image Registration. presented by John Melonakos – NAMIC Core 1 Workshop – 31/May/2007. Outline. Geodesic Tractography Review Cingulum Bundle Tractography --------------------------------------------- Fast Numerical Schemes

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PDE methods for DWMRI Analysis and Image Registration

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  1. PDE methods for DWMRI Analysis and Image Registration presented by John Melonakos – NAMIC Core 1 Workshop – 31/May/2007

  2. Outline • Geodesic Tractography Review • Cingulum Bundle Tractography --------------------------------------------- • Fast Numerical Schemes • Applications to Image Registration

  3. Contributors • Georgia Tech- • John Melonakos, Vandana Mohan, Allen Tannenbaum • BWH- • Marc Niethammer, Kate Smith, Marek Kubicki, Martha Shenton • UCI- • Jim Fallon

  4. Publications • J. Melonakos, E. Pichon, S. Angenent, A. Tannenbaum. “Finsler Active Contours”. IEEE Transactions on Pattern Analysis and Machine Intelligence. (to appear 2007). • J. Melonakos, V. Mohan, M. Niethammer, K. Smith, M. Kubicki, A. Tannenbaum. “Finsler Tractography for White Matter Connectivity Analysis of the Cingulum Bundle”. MICCAI 2007. • V. Mohan, J. Melonakos, M. Niethammer, M. Kubicki, A. Tannenbaum. “Finsler Level Set Segmentation for Imagery in Oriented Domains”. BMVC 2007 (in submission). • Eric Pichon and Allen Tannenbaum. Curve segmentation using directional information, relation to pattern detection. In IEEE International Conference on Image Processing (ICIP), volume 2, pages 794-797, 2005. • Eric Pichon, Carl-Fredrik Westin, and Allen Tannenbaum. A Hamilton-Jacobi-Bellman approach to high angular resolution diffusion tractography. In International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), pages 180-187, 2005.

  5. Directional Dependence the new length functional tangent direction This is a metric on a “Finsler” manifold if Ψ satisfies certain properties.

  6. Finsler Metrics • the Finsler properties: • Regularity • Positive homogeneity of degree one in the second variable • Strong Convexity Note: Finsler geometry is a generalization of Riemannian geometry.

  7. Closed Curves:The Flow Derivation Computing the first variation of the functional E, the L2-optimal E-minimizing deformation is:

  8. Open Curves:The Value Function Consider a seed region S½Rn, define for all target points t2Rn the value function: curves between S and t It satisfies the Hamilton-Jacobi-Bellman equation:

  9. Numerics Closed Curves Open Curves Level Set Techniques Dynamic Programming (Fast Sweeping)

  10. Finsler vs Riemann vs Euclid

  11. Outline • Geodesic Tractography Review • Cingulum Bundle Tractography --------------------------------------------- • Fast Numerical Schemes • Applications to Image Registration

  12. A Novel Approach • Use open curves to find the optimal “anchor tract” connecting two ROIs • Initialize a level set surface evolution on the anchor tract to capture the entire fiber bundle.

  13. The Cingulum Bundle • 5-7 mm in diameter • “ring-like belt” around CC • Involved in executive control and emotional processing

  14. The Data • 24 datasets from BWH (Marek Kubicki) • 12 Schizophrenics • 12 Normal Controls • 54 Sampling Directions

  15. The Algorithm Input • Locating the bundle endpoints • (work done by Kate Smith)

  16. The Algorithm Input • How the ROIs were drawn

  17. Results • Anterior View • Posterior View

  18. Results

  19. Results

  20. Results – A Statistical Note • Attempt to sub-divide the tract to find FA significance

  21. Work In Progress • Implemented a level set surface evolution to capture the entire bundle – preliminary results. • Working with Marek Kubicki and Jim Fallon to make informed subdivision of the bundle for statistical processing. • Linking the technique to segmentation work in order to connect brain structures.

  22. Outline • Geodesic Tractography Review • Cingulum Bundle Tractography --------------------------------------------- • Fast Numerical Schemes • Applications to Image Registration

  23. Contributors • Georgia Tech- • Gallagher Pryor, Tauseef Rehman, John Melonakos, Allen Tannenbaum

  24. Publications • T. Rehman, G. Pryor, J. Melonakos, I. Talos, A. Tannenbaum. “Multi-resolution 3D Nonrigid Registration via Optimal Mass Transport”. MICCAI 2007 workshop (in submission). • T. Rehman, G. Pryor, and A. Tannenbaum. Fast Optimal Mass Transport for Dynamic Active Contour Tracking on the GPU. In IEEE Conference on Decision and Control, 2007 (in submission). • G. Pryor, T. Rehman, A. Tannenbaum. BMVC 2007 (in submission).

  25. Multigrid Numerical Schemes

  26. Parallel Computing

  27. Algorithms on the GPU

  28. Parallel Computing

  29. Parallel Computing

  30. Outline • Geodesic Tractography Review • Cingulum Bundle Tractography --------------------------------------------- • Fast Numerical Schemes • Applications to Image Registration

  31. The Registration Problem • Synthetic Registration Problem

  32. Solution – The Warped Grid • Synthetic Registration Problem

  33. The Registration Problem Brain Sag Registration Problem • Before • After

  34. Solution – The Warped Grid

  35. Speedup A 128^3 registration in less than 15 seconds

  36. Key Conclusions • Multigrid algorithms on the GPU can dramatically increase performance • We used Optimal Mass Transport for registration, but other PDEs may also be implemented in this way

  37. Questions?

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